The water diet requires one to drink two cups of water every half hour from when one gets up until one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights ( in pounds) are Person 1 2 3 4 Weight before diet 180 125 240 150 Weight after diet 170 130 215 152 For the population of all adults, assume that the weights loss after six weeks on the diet ( weight before beginning the diet---weight after six weeks on the diet) is Normally distributed with mean μ.

a. Test the hypothesis if the diet leads to weight loss

A homogeneous sphere S, a uniform cylinder C, and a thin pipe P are in contact when they are released from rest on the incline shown. Knowing that all three objects roll without slipping, determine, after 9s of motion, if theta=27 degrees, Find

1. acceleration of sphere down the incline (m/s^2)
2. acceleration of pipe down the incline (m/s^2)
3. The distance between the centers of the cylinder and the sphere (m)
4. Acceleration of cylinder down the incline (m/s^2)
5. the distance between the centers of the pipe and the cylinder (m)

Q1: A cyclist collected the below data on RPMs during his ride:

58 56 50 60 55 50 52 53 59 53 55 57 57 63 48
55 47 47 52 54 53 55 46 55 56 50 55 50 57 54
68 50 62 64 53 50 64 59 61 55 53 41 57 53 50

w. Create a one-sided interval that will contain 99% of the RPMs, with 95% confidence.

x. Create a two-sided 90% interval on the RPM collected in the next test.

y. Create a 90% confidence interval on the standard deviation of the collected RPMs.

z. Create a two-sided interval that is 95% confident on containing the RPMs of all of the next five tests.

Apple Corporation is structured into three divisions: Austin, Brown and Caden. Each division operates as a separate stand-alone business, and is designated as an investment centre. The company uses return on investment (ROI) to evaluate the performance of each division. For the purpose of calculating divisional ROI, invested capital is defined as total assets (net book value) less current liabilities, and divisional operating profits after tax are used. Each division is required to achieve an ROI of at least 9%.

The following data relates to the financial performance of the divisions for the year of 2019:

Both Austin and Brown mainly operate education centers with focus on conducting computer and IT courses. Major assets of Austin Division include computer equipment, popular software and furniture and fixtures. All these assets have been used since the business was set up in 2016. No additional purchase of new assets was made.

Although Brown operates in a similar business, it has different operational philosophy. Brown leases its computer equipment and software in order to have the most updated IT facilities for their customers. Therefore, the lease (rental) expenses account for a high percentage of its total operating expenses.

Caden runs two restaurants which were newly set in 2019. The target customers are the highclass clusters. Therefore, high amount was spent on decent and splendid furniture and decoration.

Based on the ROI calculation, the management would rank Brown as the top performer while Caden is required to put significant effort to improve its performance.

REQUIRED:

1) Suggest TWO points in the case that needs to be taken into account when interpreting divisional performance by using ROI.

2) State and explain any action for Austin and Caden Division to improve their ROIs but it will result in UNDERSIRABLE operating results (ONE action for each Division).

3) Suggest TWO ways to minimize the negative behavioral effects of ROI (use examples in your answer.

Cain Components manufactures and distributes various plumbing products used in homes and other buildings. Over time, the production staff has noticed that products they considered easy to make were difficult to sell at margins considered reasonable, while products that seemed to take a lot of staff time were selling well despite recent price increases. A summer intern has suggested that the cost system might be providing misleading information.

The controller decided that a good summer project for the intern would be to develop, in one self-contained area of the plant, an alternative cost system with which to compare the current system. The intern identified the following cost pools and, after discussion with some plant personnel, appropriate cost drivers for each pool. There were:

In this particular area, Cain produces two of its many products: Standard and Deluxe. The following are data for production for the latest full year of operations.

Required:

a. The current cost accounting system charges overhead to products based on machine-hours. What unit product costs will be reported for the two products if the current cost system continues to be used?

Direct Costs: Standard? Deluxe?

Overhead: Standard? Deluxe?

Number of Units: Standard? Deluxe?

b. The intern suggests an ABC system using the cost drivers identified above. What unit product costs will be reported for the two products if the ABC system is used?

Direct Costs: Standard? Deluxe?

Receiving: Standard? Deluxe?

Manufacturing: Standard? Deluxe?

Machine Set Up: Standard? Deluxe?

Shipping: Standard? Deluxe?

Number of Units: Standard? Deluxe?

Assuming that the following table represents the investment demand schedules for Country A and Country B.

• Plot the respective investment demand curves of Country A and Country B. How is investment related to interest rate? How does this manifest in the graph?

• How would you characterize the responsiveness of investment spending to the interest rates in Country A compared with Country B?

• Assuming an MPC of 75%, what would be the effect on real GDP in Country A and Country B if real interest rates decline from 8% to 6%?

The following data are the heights of fathers and their sons in inches. The father's height is his height when he was the same age as the son.

a. A geneticist might wonder if there is a tendency for tall fathers to have tall sons and short fathers to have short sons. Answer this question by computing the appropriate statistic and testing it for statistical significance. (Hint: The statistic will be much easier to compute if you subtract 40 from each of the scores. Doing so will not affect the value of the statistic.)

b. Can you use the height of a father to predict the height of his son? Compute the regression equation for predicting sons’ heights from fathers’ heights. Use this equation to predict the height of a son whose father is 46 inches tall.

c. If you had a father who had a height of 25" when he was the same age as his son, should you use the regression equation to predict the son’s height? Why or why not?

d. An environmentalist might wonder if there is a tendency for generations to get taller. Are sons taller than their fathers were at the same age? What statistical test would be most appropriate for answering this question. (Hint: You will need to recall some previous lessons to get this one correct.)

Empire Electric Company (EEC) uses only debt and common equity. It can borrow unlimited amounts at an interest rate of r_d = 11% as long as it finances at its target capital structure, which calls for 45% debt and 55% common equity. Its last dividend (D₀) was $1.70, its expected constant growth rate is 5%, and its common stock sells for $29. EEC's tax rate is 25%. Two projects are available: Project A has a rate of return of 14%, and Project B's return is 8%. These two projects are equally risky and about as risky as the firm's existing assets.

1. What is its cost of common equity? Do not round intermediate calculations. Round your answer to two decimal places.

   %

2. What is the WACC? Do not round intermediate calculations. Round your answer to two decimal places.

   part two

   barton Industries expects that its target capital structure for raising funds in the future for its capital budget will consist of 40% debt, 5% preferred stock, and 55% common equity. Note that the firm's marginal tax rate is 25%. Assume that the firm's cost of debt, r_d, is 10.3%, the firm's cost of preferred stock, r_p, is 9.5% and the firm's cost of equity is 12.9% for old equity, r_s, and 13.2% for new equity, r_e. What is the firm's weighted average cost of capital (WACC₁) if it uses retained earnings as its source of common equity? Do not round intermediate calculations. Round your answer to two decimal places.

   %

   What is the firm’s weighted average cost of capital (WACC₂) if it has to issue new common stock? Do not round intermediate calculations. Round your answer to two decimal places.

   %

Two fuel additives are being tested to determine their effect on gasoline mileage. Seven cars were tested with additive 1 and nine cars were tested with additive 2. The following data show the miles per gallon obtained with the two additives.

Use α = 0.05 and the MWW test to see whether there is a significant difference between gasoline mileage for the two additives.

Find the value of the test statistic:

W = ?

Find the p-value. (Round your answer to four decimal places.):

p-value = ?

Two fuel additives are being tested to determine their effect on gasoline mileage. Seven cars were tested with additive 1 and nine cars were tested with additive 2. Data: Additive 1 - 17.3,18.4, 19.1, 17.7, 17.2, 17.6, 18.5; Additive 2 - 18.7, 18.8, 20.3, 20.0, 21.1, 18.7, 18.8, 20.7, 21.2. The following data show the miles per gallon obtained with the two additives. I am struggling to determine the p-value.